Probing the littlest Higgs model with $T$ parity using di-Higgs events through $Z_H$-pair production at the LHC in NLO QCD

We investigate the di-Higgs events through $Z_H$-pair production at the CERN Large Hadron Collider including the pure next-to-leading order (NLO) QCD correction and the $gg$-fusion contribution in the framework of the littlest Higgs model with $T$ parity. We employ the diagram subtraction scheme in the QCD NLO calculations to avoid double counting and keep the convergence of the perturbative QCD description for the $Z_H$-pair production. We investigate the dependence of the leading order and QCD corrected integrated cross sections on the renormalization/factorization scale, and find that the total QCD corrections slightly reduce the scale uncertainty in the plotted range. By considering the subsequent decays of the intermediately produced $Z_H$ bosons and adopting the exclusive four-$b$-jet event selection criterion, the QCD correction provides considerable enhancement of the kinematic distributions for final decay products. We find that it is possible to select the signature of the $Z_H$-pair production from possible standard model background by taking proper kinematic cuts.

Figure 1

The production structure for the $b\overline{b}b\overline{b}+{\cancel{E}}_T$ signature via $Z_H$-pair production at the hadron collider.

Figure 2

The LO Feynman diagrams for the partonic process $q\overline{q}\to Z_H{Z}_H$.

Figure 3

The one-loop Feynman diagrams for the partonic process $q\overline{q}\to Z_H{Z}_H$.

Figure 4

The Feynman diagrams for the real gluon emission process $q\overline{q}\to Z_H{Z}_H+g$.

Figure 5

The tree-level Feyman diagrams for the $qg\to Z_H{Z}_H+q$ partonic process. The diagrams of (a)–(b) do not include a $q_{-}$-resonance propagator, while each of the diagrams in (c)–(f) contains a possible $q_{-}$-resonance propagator.

Figure 6

The representative QCD one-loop Feynman diagrams for the partonic process $gg\to Z_H{Z}_H$, where $q=u,d,c,s,b,t$ and $q_{-}=u_{-},d_{-},c_{-},s_{-},b_{-},t_{-}$.

Figure 7

The renormalization/factorization scale dependence of the LO, pure NLO QCD, total QCD corrected total cross sections, and the corresponding $K$-factors for the process $pp\to Z_H{Z}_H+X$ at the 14 TeV LHC with ${\mu }_0=m_{Z_H}$.

Figure 8

The LO, total QCD corrected integrated cross sections, and the corresponding $K$-factor for the process $pp\to Z_H{Z}_H+X$ at the 14 TeV LHC as the functions of the symmetry breaking scale $f$.

Figure 9

The LO, total QCD corrected distributions of the leading Higgs transverse momentum and the corresponding $K$-factor for the $pp\to Z_H{Z}_H\to A_H{A}_{H}hh+X$ process at the $\sqrt{s}=14\mathrm{TeV}$ LHC.

Figure 10

The LO, total QCD corrected distributions of the Higgs pair invariant mass and the corresponding $K$-factor for the $pp\to Z_H{Z}_H\to A_H{A}_{H}hh+X$ process at the $\sqrt{s}=14\mathrm{TeV}$ LHC.

Figure 11

The LO, total QCD corrected distributions of the transverse momentum of the leading $b$ jet ($b_1$) and the corresponding $K$-factor for the $pp\to Z_H{Z}_H\to A_H{A}_{H}hh\to A_H{A}_{H}b\overline{b}b\overline{b}+X$ process at the $\sqrt{s}=14\mathrm{TeV}$ LHC by adopting the exclusive four-$b$-jet event selection scheme.

Figure 12

The LO, total QCD corrected distributions of rapidity of the leading $b$ jet ($b_1$) and the corresponding $K$-factor for the $pp\to Z_H{Z}_H\to A_H{A}_{H}hh\to A_H{A}_{H}b\overline{b}b\overline{b}+X$ process at the $\sqrt{s}=14\mathrm{TeV}$ LHC by adopting the exclusive four-$b$-jet event selection scheme.

Figure 13

The LO, total QCD corrected distributions of the invariant mass of the leading and subleading $b$ jets and the corresponding $K$-factor for the $pp\to Z_H{Z}_H\to A_H{A}_{H}hh\to A_H{A}_{H}b\overline{b}b\overline{b}+X$ process at the $\sqrt{s}=14\mathrm{TeV}$ LHC by adopting the exclusive four-$b$-jet event selection scheme.

Figure 14

The normalized LO, total QCD corrected $H_T$ distributions for the signal process $pp\to Z_H{Z}_H\to A_H{A}_{H}hh\to A_H{A}_{H}b\overline{b}b\overline{b}+X$, the normalized LO $H_T$ distribution for the $pp\to Zb\overline{b}\to b\overline{b}b\overline{b}+X$, and the normalized NLO QCD corrected $H_T$ distribution for the $pp\to b\overline{b}b\overline{b}+X$ at the $\sqrt{s}=14\mathrm{TeV}$ LHC. There the normalized NLO QCD corrected $H_T$ distribution for the SM background processes $pp\to b\overline{b}b\overline{b}+X$ is obtained from Ref. [47].